Since politics is a game, New Yorkers should be relieved: The Yankees have strong competition for the title of “America’s Most Embarrassing Team” from the Republican Party in Washington.

Most Republicans are acting rationally, handling the complexities of the party’s political position with care and cleverness. They’re working to thread the needle between standing true to general principle and finding at least stopgap solutions on issues where there is no common ground with Democrats.

But just as it takes only one bad infield play and one hanging curve ball to take the Yankees down, it only takes a few politicians to take a party down — especially when the mainstream media are gunning for that party.

The “Can’t anybody play this game?” issue of the week is gun control.

You may not have noticed, but there has been a marked shift in the approach to the gun issue over the past couple of months — by Democrats.

In the wake of the Newtown massacre, the drive to pass major restrictions received almost universal support from those who still deliberately or ignorantly or self-righteously choose to confuse gun ownership (as many as 45 percent of American households) with criminal offenses involving a gun (8 percent of all crimes).

And off the shelf came the usual set of proposals, some of which had been on the books until a gun-control law expired in 2005. There was the banning of “assault weapons,” a nonexistent category created by poll testing 20 years ago. There was the limitation on high-capacity magazines, which sounds good but is meaningless.

These were nonstarters at the federal level, but not because of Republicans: Rather, Democratic senators facing tough re-election campaigns in more conservative states (where gun owners are usually an outright majority of the population) reared in horror at the prospect of being forced to choose between the wishes of the president and big-money donors . . . and the actual voters in their states.

With that in mind, Senate Majority Leader Harry Reid removed any ban on rifles or bullet-holders from a bill whose final contents are yet to be determined. This was a concession to reality and an example of how representative politics actually works apart from the screaming temper tantrums of pompous quick-fixers for whom a gun is some kind of negative fetish.

And there the matter stood — with Reid stuck with a bill the president wants, but one whose success might lead to the defeats of enough senators to lose him his status as majority leader.

That’s about as good as an opposition party could hope for.

Until last week, that is — when a few Republican senators with ideological blinders and perverse incentives decided to raise the stakes and declare that they’d filibuster any gun bill that came to the floor of the Senate.

There was no political need for such a declaration. By making it, Sens. Mike Lee of Utah and Ted Cruz of Texas instantly gave the president and gun controllers a way back in the game — by declaring that the GOP was using smelly backdoor tactics to prevent any kind of vote.

The president went on the attack, giving a fiery speech about the dangers to our children. Meanwhile, a patient pro-gun Democratic senator from West Virginia named Joe Manchin had been working on a face-saving bit of folderol — a provision to expand background checks before gun purchases.

Going from banning semiautomatic weapons to adding some new background checks was a mark of just how far the debate had shifted away from the immediate world-changing ardor right after Newtown.

It’s a no-brainer: Background checks are popular. Very popular — like 80-90 percent popular. Majorities of gun owners support background checks.

Rather than being able to take credit for having moved the gun debate into an uncontroversial middle ground, the GOP senators and some of their supporters have decided to snatch defeat from the jaws of victory. They’re acting as though background checks are a form of confiscation.

They are calling Sen. Pat Toomey, a Republican from Pennsylvania who agreed to co-sponsor Manchin’s proposal, a traitor and a sellout — Pat Toomey, the very conservative former head of the Club for Growth, the man who knocked off the anti-conservative Arlen Specter in 2010!

These sorts of ideological-revenge declarations explain Lee’s and Cruz’s confrontationalist strategy, because they point out the perverse incentives enjoyed by far too many politicians on the Right today: They are celebrated for being unreasonable.